Elements Of Algebraic Topology [Paperback]

James R. Munkres (Author)

Product Details

• Paperback: 464 pages
• Publisher: Westview Press (January 1, 1996)
• Language: English
• ISBN-10: 0201627280
• ISBN-13: 978-0201627282
• Product Dimensions: 8.9 x 6 x 1.1 inches
• Shipping Weight: 1.5 pounds (View shipping rates and policies)
• Average Customer Review: 3.8 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #717,099 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

31 of 32 people found the following review helpful:

4.0 out of 5 stars Excellent text on homology and cohomology, December 22, 1998

By 

Kevin M. Iga (Pepperdine University (Malibu, CA)) - See all my reviews
(REAL NAME)   

This review is from: Elements Of Algebraic Topology (Paperback)

Algebraic topology is a tough subject to teach, and this book does a very good job. Some prerequisites, however, are essential:

* point set topology (e.g. in Munkres' Topology)

* Abstract algebra

* Mathematical maturity to be willing to follow a definition and argument even when it seems like a weird side-track

In addition, this would not be the first book I would recommend to those interested in algebraic topology. First might be Massey's "Algebraic Topology: and Introduction" that introduces the fundamental group (conceptually easier than homology and cohomology).

At some point, however, a prospective student in topology will have to learn homological algebra and this provides the most concrete approach I know to the subject.

Algebraic topology is a lot of fun, but many of the previous textbooks had not given that impression. This one does.

15 of 15 people found the following review helpful:

4.0 out of 5 stars A little incomplete, March 24, 2000

By 

Bernardo Vargas - See all my reviews

This review is from: Elements Of Algebraic Topology (Paperback)

This well written text is one of the standard references in algebraic topology courses because of its conciseness, and I find it very useful as a reference text.

However I think it is a little incomplete because of several reasons.

(1)It pays no attention to one basic concept of algebraic topology: the fundamental group.

(2) It doesn't cover ^Cech homology, important in other areas, like dimension theory for example.

(3) It doesn't stress the most important feature of algebraic topology: its connection to other areas of mathematics (analysis, differential geometry, etc.).

(4) Its list of references is too short, and lacks almost completely HISTORICAL references which are always important to become an expert in any field.

Conclusion: a good reference on homology and cohomology essentials, but not "the" reference on algebraic topology as a whole.

12 of 13 people found the following review helpful:

3.0 out of 5 stars The book binding is horrible, February 4, 2000

By A Customer

This review is from: Elements Of Algebraic Topology (Paperback)

The material in the book (homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in manifolds, applications to classical theorems of point-set topology) is for the most part solid. However...

- Munkres really belabors the simplicial theory, and it gets to be quite painful (especially the *CHAPTER* on the topological invariance of simplicial homology groups).

- Some very important topics (homotopy theory, fiber bundles) are not at all discussed.

- The book binding is horrible -- my copy is in two pieces, with several loose pages, and I don't think the hardcover edition is still in print.